Triangle XYZ was dilated by a scale factor of 2 to create triangle ACB and tan ∠X = 5 over 2 and 5 tenths. Triangles XYZ and ACB; angles Y and C both measure 90 degrees, angles A and X are congruent.

Part A: Use complete sentences to explain the special relationship between the trigonometric ratios of triangles XYZ and ABC. You must show all work and calculations to receive full credit. (5 points)

Part B: Explain how to find the measures of segments AC and CB. You must show all work and calculations to receive full credit. (5 points)

Step-by-step explanation:

As for the angles of both triangles; they’re the same. The sides are 1:2.

I’m giving you formulas that are labeled: side a shortest

” b mid length

” c hypotenuse

angle α(alpha) opposite side a

” β(beta) ” ” b

” γ(gamma) ” ” c

A major formula for rt triangles is: a^2+b^2=c^2.

*Another is: a/sinα=b/sinβ=c/sinγ.

Remember α+β+γ=180°.

As for sides a&b use the above formula.

As for <ACB; the angle is γ which is a rt <.

Given: tan<x=5/2+1/2=6/2=3atan=71.565……….°=β. So α=18.44…….°. γ= rt angle.

To get the sides use the formulas at *.